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Backward uniqueness of stochastic parabolic like equations driven by Gaussian multiplicative noise

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  • Barbu, Viorel
  • Röckner, Michael

Abstract

One proves here the backward uniqueness of solutions to stochastic semilinear parabolic equations and also for the tamed Navier–Stokes equations driven by linearly multiplicative Gaussian noises. Applications to approximate controllability of nonlinear stochastic parabolic equations with initial controllers are given. The method of proof relies on the logarithmic convexity property known to hold for solutions to linear evolution equations in Hilbert spaces with self-adjoint principal part.

Suggested Citation

  • Barbu, Viorel & Röckner, Michael, 2016. "Backward uniqueness of stochastic parabolic like equations driven by Gaussian multiplicative noise," Stochastic Processes and their Applications, Elsevier, vol. 126(7), pages 2163-2179.
    • Handle: RePEc:eee:spapps:v:126:y:2016:i:7:p:2163-2179
    DOI: 10.1016/j.spa.2016.01.007
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    References listed on IDEAS

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    1. Brzeźniak, Zdzisław & Neklyudov, Misha, 2013. "Backward uniqueness and the existence of the spectral limit for linear parabolic SPDEs," Stochastic Processes and their Applications, Elsevier, vol. 123(5), pages 1851-1870.
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